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JEE Main 3 April 2025 Shift 2 Question Paper with Answers

3 April 2025 · April session · 75 questions

The complete JEE Main 3 April 2025 Shift 2 paper — all 75 questions with the correct answer for each, tagged to the chapter it tests. Free to read, no account needed.

Physics
25
Chemistry
25
Mathematics
25

Physics — JEE Main 3 April 2025 Shift 2

Q1·Physics·Magnetism and MatterSingle correct
A magnetic dipole experiences a torque of 80380\sqrt3803​ N m when placed in a uniform magnetic field in such a way that the dipole moment makes an angle of 60∘60^\circ60∘ with the magnetic field. The potential energy of the dipole is:
  1. (A)80 J
  2. (B)−403-40\sqrt3−403​ J
  3. (C)−60-60−60 J
  4. (D)−80-80−80 J

Correct answer: (D)

Step-by-step solution →
Q2·Physics·WavesSingle correct
In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:
  1. (A)335 m/s
  2. (B)370 m/s
  3. (C)340 m/s
  4. (D)360 m/s

Correct answer: (D)

Step-by-step solution →
Q3·Physics·Work, Energy and PowerSingle correct
Two cylindrical vessels of equal cross sectional area of 2 m22\,\mathrm{m}^22m2 contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is: (Density of water is 103 kg/m310^3\,\mathrm{kg/m^3}103kg/m3 and g=10 m/s2g=10\,\mathrm{m/s^2}g=10m/s2)
  1. (A)1×1051\times10^51×105 J
  2. (B)4×1054\times10^54×105 J
  3. (C)6×1056\times10^56×105 J
  4. (D)8×1058\times10^58×105 J

Correct answer: (D)

Step-by-step solution →
Q4·Physics·Wave OpticsSingle correct
Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:
  1. (A)(22+1):(22−1)(2\sqrt2+1):(2\sqrt2-1)(22​+1):(22​−1)
  2. (B)(3+22):(3−22)(3+2\sqrt2):(3-2\sqrt2)(3+22​):(3−22​)
  3. (C)9:19:19:1
  4. (D)3:13:13:1

Correct answer: (B)

Step-by-step solution →
Q5·Physics·ThermodynamicsSingle correct
An ideal gas exists in a state with pressure P0P_0P0​, volume V0V_0V0​. It is isothermally expanded to 4 times of its initial volume (V0)(V_0)(V0​), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is:
  1. (A)P0V0(2ln⁡2−0.75)P_0V_0(2\ln 2-0.75)P0​V0​(2ln2−0.75)
  2. (B)P0V0(ln⁡2−0.75)P_0V_0(\ln 2-0.75)P0​V0​(ln2−0.75)
  3. (C)P0V0(2ln⁡2−0.25)P_0V_0(2\ln 2-0.25)P0​V0​(2ln2−0.25)
  4. (D)P0V0(2ln⁡2+0.25)P_0V_0(2\ln 2+0.25)P0​V0​(2ln2+0.25)

Correct answer: (A)

Step-by-step solution →
Q6·Physics·Wave OpticsSingle correct
Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is:
  1. (A)8:18:18:1
  2. (B)9:19:19:1
  3. (C)3:13:13:1
  4. (D)4:14:14:1

Correct answer: (D)

Step-by-step solution →
Q7·Physics·Atoms and NucleiSingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason R: The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both A and R are true but R is NOT the correct explanation of A.
  2. (B)A is false but R is true.
  3. (C)Both A and R are true and R is the correct explanation of A.
  4. (D)A is true but R is false.

Correct answer: (C)

Step-by-step solution →
Q8·Physics·Capacitors and DielectricsSingle correct
Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)
  1. (A)600
  2. (B)200
  3. (C)400
  4. (D)100

Correct answer: (B)

Step-by-step solution →
Q9·Physics·Geometrical OpticsSingle correct
A monochromatic light of frequency 5×10145\times10^{14}5×1014 Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be:
  1. (A)300 nm
  2. (B)600 nm
  3. (C)400 nm
  4. (D)500 nm

Correct answer: (A)

Step-by-step solution →
Q10·Physics·Work, Energy and PowerSingle correct
Consider two blocks A and B of masses m1=10m_1=10m1​=10 kg and m2=5m_2=5m2​=5 kg are placed on a frictionless table. The block A moves with a constant speed v=3v=3v=3 m/s towards the block B kept at rest. A spring with spring constant k=3000k=3000k=3000 N/m is attached with the block B. After the collision, suppose that the blocks A and B, along with the spring in contact compression state, move together, then the compression in the spring is (neglect the mass of the spring):
  1. (A)0.2 m
  2. (B)0.4 m
  3. (C)0.1 m
  4. (D)0.3 m

Correct answer: (C)

Step-by-step solution →
Q11·Physics·KinematicsSingle correct
A particle is projected with velocity uuu so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g\dfrac{nu^2}{25g}25gnu2​, where the value of nnn is: (Given 'ggg' is the acceleration due to gravity.)
  1. (A)6
  2. (B)18
  3. (C)12
  4. (D)24

Correct answer: (D)

Step-by-step solution →
Q12·Physics·Properties of Solids and LiquidsSingle correct
A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45×10−22.45\times10^{-2}2.45×10−2 m/s while falling under gravity through an oil of density 925 kg m−3925\,\mathrm{kg\,m^{-3}}925kgm−3. Take density of steel as 7825 kg m−37825\,\mathrm{kg\,m^{-3}}7825kgm−3 and ggg as 9.8 m/s29.8\,\mathrm{m/s^2}9.8m/s2. The viscosity of the oil in SI unit is:
  1. (A)2.18
  2. (B)2.38
  3. (C)1.68
  4. (D)1.99

Correct answer: (D)

Step-by-step solution →
Q13·Physics·Electronic DevicesSingle correct
The truth table corresponding to the circuit given below is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q14·Physics·KinematicsSingle correct
A particle moves along the x-axis and has its displacement xxx varying with time ttt according to the equation x=c0(t2−2)+c(t−2)2x=c_0(t^2-2)+c(t-2)^2x=c0​(t2−2)+c(t−2)2, where c0c_0c0​ and ccc are constants of appropriate dimensions. Then, which of the following statements is correct?
  1. (A)The acceleration of the particle is 2c02c_02c0​.
  2. (B)The acceleration of the particle is 2c2c2c.
  3. (C)The initial velocity of the particle is 4c4c4c.
  4. (D)The acceleration of the particle is 2(c+c0)2(c+c_0)2(c+c0​).

Correct answer: (D)

Step-by-step solution →
Q15·Physics·Alternating CurrentsSingle correct
An electric bulb rated as 100 W-220 V is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:
  1. (A)0.64 A
  2. (B)0.45 A
  3. (C)2.2 A
  4. (D)0.32 A

Correct answer: (A)

Step-by-step solution →
Q16·Physics·Units and MeasurementsSingle correct
Match the LIST-I (Physical quantities and constants) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:
LIST-I (Physical quantities and constants)LIST-II (Dimensional formula)
A.Boltzmann constantI.ML2T−1ML^2T^{-1}ML2T−1
B.Coefficient of viscosityII.MLT−3K−1MLT^{-3}K^{-1}MLT−3K−1
C.Planck's constantIII.ML2T−2K−1ML^2T^{-2}K^{-1}ML2T−2K−1
D.Thermal conductivityIV.ML−1T−1ML^{-1}T^{-1}ML−1T−1
  1. (A)A-III, B-IV, C-I, D-II
  2. (B)A-II, B-III, C-IV, D-I
  3. (C)A-III, B-II, C-I, D-IV
  4. (D)A-III, B-IV, C-II, D-I

Correct answer: (A)

Step-by-step solution →
Q17·Physics·Kinetic Theory of GasesSingle correct
Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1∘1^\circ1∘C. Its initial temperature must be:
  1. (A)25∘25^\circ25∘C
  2. (B)2500 K
  3. (C)250 K
  4. (D)250∘250^\circ250∘C

Correct answer: (C)

Step-by-step solution →
Q18·Physics·Current ElectricitySingle correct
A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is 91.6%, then the loss of power in units of cal/s is:
  1. (A)4
  2. (B)8.4
  3. (C)2
  4. (D)6.2

Correct answer: (C)

Step-by-step solution →
Q19·Physics·Work, Energy and PowerSingle correct
A block of mass 1 kg, moving along the x-axis with speed v=10v=10v=10 m/s enters a rough region ranging from x=0.1x=0.1x=0.1 m to x=1.9x=1.9x=1.9 m. The retarding force acting on the block in this range is Fr=−kxF_r=-kxFr​=−kx N, with k=10k=10k=10 N/m. Then the final speed of the block as it crosses the rough region is:
  1. (A)10 m/s
  2. (B)4 m/s
  3. (C)6 m/s
  4. (D)8 m/s

Correct answer: (D)

Step-by-step solution →
Q20·Physics·Magnetic Field of CurrentSingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If oxygen ion (O−)(O^-)(O−) and Hydrogen ion (H+)(H^+)(H+) enter normal to the magnetic field with equal momentum, then the path of O−O^-O− ion has a smaller curvature than that of H+H^+H+. Reason R: A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is true but R is false.
  2. (B)Both A and R are true but R is NOT the correct explanation of A.
  3. (C)A is false but R is true.
  4. (D)Both A and R are true and R is the correct explanation of A.

Correct answer: (A)

Step-by-step solution →
Q21·Physics·Geometrical OpticsInteger
Light from a point source in air falls on a spherical glass surface (refractive index μ=1.5\mu=1.5μ=1.5 and radius of curvature =50=50=50 cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is __________ m.

Correct answer: 4

Step-by-step solution →
Q22·Physics·Properties of Solids and LiquidsInteger
The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is nnn times the volume of the bubble B, then, the value of nnn is __________.

Correct answer: 8

Step-by-step solution →
Q23·Physics·Current ElectricityInteger
Two cells of emf 1 V and 2 V and internal resistance 2 Ω\OmegaΩ and 1 Ω\OmegaΩ, respectively, are connected in series with an external resistance of 6 Ω\OmegaΩ. The total current in the circuit is I1I_1I1​. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is I2I_2I2​. The value of (I1I2)\left(\dfrac{I_1}{I_2}\right)(I2​I1​​) is x3\dfrac{x}{3}3x​. The value of xxx is __________.

Correct answer: 4

Step-by-step solution →
Q24·Physics·Atoms and NucleiInteger
An electron in the hydrogen atom initially in the fourth excited state makes a transition to nthn^{th}nth energy state by emitting a photon of energy 2.86 eV. The integer value of nnn will be __________.

Correct answer: 2

Step-by-step solution →
Q25·Physics·Units and MeasurementsInteger
A physical quantity C is related to four other quantities p, q, r and s as follows C=pq2r3sC=\dfrac{pq^2}{r^3\sqrt s}C=r3s​pq2​. The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %.

Correct answer: 15

Step-by-step solution →

Chemistry — JEE Main 3 April 2025 Shift 2

Q26·Chemistry·Some Basic Concepts in ChemistrySingle correct
40 mL of a mixture of CH3COOHCH_3COOHCH3​COOH and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct?
  1. (A)The concentration of CH3COOHCH_3COOHCH3​COOH in the original mixture is 0.005 M
  2. (B)The concentration of HCl in the original mixture is 0.005 M
  3. (C)CH3COOHCH_3COOHCH3​COOH is neutralised first followed by neutralisation of HCl
  4. (D)Point 'C' indicates the complete neutralisation of HCl

Correct answer: (B)

Step-by-step solution →
Q27·Chemistry·Some Basic Concepts in ChemistrySingle correct
10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 mole of HCl and made the volume upto the mark with distilled water. The solution in this flask is:
  1. (A)0.2 M NaCl solution
  2. (B)20 M HCl solution
  3. (C)10 M HCl solution
  4. (D)Neutral solution

Correct answer: (B)

Step-by-step solution →
Q28·Chemistry·BiomoleculesSingle correct
Fat soluble vitamins are: A. Vitamin B1B_1B1​ B. Vitamin C C. Vitamin E D. Vitamin B12B_{12}B12​ E. Vitamin K Choose the correct answer from the options given below:
  1. (A)C & D Only
  2. (B)A & B Only
  3. (C)B & C Only
  4. (D)C & E Only

Correct answer: (D)

Step-by-step solution →
Q29·Chemistry·Classification of Elements and Periodicity in PropertiesSingle correct
Match the LIST-I (Family) with LIST-II (Symbol of Element). Choose the correct answer from the options given below:
LIST-I (Family)LIST-II (Symbol of Element)
A.Pnicogen (group 15)I.Ts
B.ChalcogenII.Og
C.HalogenIII.Lv
D.Noble gasIV.Mc
  1. (A)A-IV, B-I, C-II, D-III
  2. (B)A-IV, B-III, C-I, D-II
  3. (C)A-III, B-II, C-IV, D-I
  4. (D)A-II, B-III, C-I, D-IV

Correct answer: (B)

Step-by-step solution →
Q30·Chemistry·Atomic StructureSingle correct
For electron in '2s' and '2p' orbitals, the orbital angular momentum values, respectively are:
  1. (A)2 h2π\sqrt2\,\dfrac{h}{2\pi}2​2πh​ and 0
  2. (B)h2π\dfrac{h}{2\pi}2πh​ and 2 h2π\sqrt2\,\dfrac{h}{2\pi}2​2πh​
  3. (C)000 and 6 h2π\sqrt6\,\dfrac{h}{2\pi}6​2πh​
  4. (D)000 and 2 h2π\sqrt2\,\dfrac{h}{2\pi}2​2πh​

Correct answer: (D)

Step-by-step solution →
Q31·Chemistry·Some Basic Concepts in ChemistrySingle correct
Compounds that should not be used as primary standards in titrimetric analysis are: A. Na2Cr2O7Na_2Cr_2O_7Na2​Cr2​O7​ B. Oxalic acid C. NaOH D. FeSO4⋅6H2OFeSO_4\cdot 6H_2OFeSO4​⋅6H2​O E. Sodium tetraborate Choose the most appropriate answer from the options given below:
  1. (A)B and D Only
  2. (B)D and E Only
  3. (C)C, D and E Only
  4. (D)A, C and D Only

Correct answer: (D)

Step-by-step solution →
Q32·Chemistry·Aldehydes and KetonesSingle correct
The major product (P) in the following reaction is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q33·Chemistry·Organic Compounds Containing HalogensSingle correct
In the following series of reactions identify the major products A & B respectively.
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q34·Chemistry·Redox Reactions and ElectrochemistrySingle correct
The standard cell potential (Ecell⊖)(E^{\ominus}_{cell})(Ecell⊖​) of a fuel cell based on the oxidation of methanol in air that has been used to power a television relay station is measured as 1.21 V. The standard half cell reduction potential for O2O_2O2​ (EO2/H2O∘)\left(E^{\circ}_{O_2/H_2O}\right)(EO2​/H2​O∘​) is 1.229 V. Choose the correct statement:
  1. (A)The standard half cell reduction potential for the reduction of CO2CO_2CO2​ (ECO2/CH3OH∘)\left(E^{\circ}_{CO_2/CH_3OH}\right)(ECO2​/CH3​OH∘​) is 19 mV
  2. (B)Oxygen is formed at the anode.
  3. (C)Reactants are fed at one go to each electrode.
  4. (D)Reduction of methanol takes place at the cathode.

Correct answer: (A)

Step-by-step solution →
Q35·Chemistry·Coordination CompoundsSingle correct
Identify the diamagnetic octahedral complex ions from below: A. [Mn(CN)6]3−[Mn(CN)_6]^{3-}[Mn(CN)6​]3− B. [Co(NH3)6]3+[Co(NH_3)_6]^{3+}[Co(NH3​)6​]3+ C. [Fe(CN)6]4−[Fe(CN)_6]^{4-}[Fe(CN)6​]4− D. [Co(H2O)3F3][Co(H_2O)_3F_3][Co(H2​O)3​F3​] Choose the correct answer from the options given below:
  1. (A)B and D Only
  2. (B)A and D Only
  3. (C)A and C Only
  4. (D)B and C Only

Correct answer: (D)

Step-by-step solution →
Q36·Chemistry·Purification and Characterisation of Organic CompoundsSingle correct
In Dumas' method for estimation of nitrogen, 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is: (Given: Aqueous tension at 300 K = 15 mm Hg)
  1. (A)15.71%
  2. (B)20.95%
  3. (C)17.46%
  4. (D)7.85%

Correct answer: (A)

Step-by-step solution →
Q37·Chemistry·Some Basic Concepts in ChemistrySingle correct
Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is: (Given: Molar mass of Mg is 24 g mol−1^{-1}−1)
  1. (A)235.7 g
  2. (B)0.24 mg
  3. (C)236 mg
  4. (D)2.444 g

Correct answer: (C)

Step-by-step solution →
Q38·Chemistry·BiomoleculesSingle correct
Given below are two statements: Statement I: Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes. Statement II: Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is false but Statement II is true
  2. (B)Statement I is true but Statement II is false
  3. (C)Both Statement I and Statement II are true
  4. (D)Both Statement I and Statement II are false

Correct answer: (B)

Step-by-step solution →
Q39·Chemistry·d- and f-Block ElementsSingle correct
Given below are two statements: Statement I: CrO3CrO_3CrO3​ is a stronger oxidizing agent than MoO3MoO_3MoO3​. Statement II: Cr(VI) is more stable than Mo(VI). In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is false but Statement II is true
  2. (B)Statement I is true but Statement II is false
  3. (C)Both Statement I and Statement II are true
  4. (D)Both Statement I and Statement II are false

Correct answer: (B)

Step-by-step solution →
Q40·Chemistry·Electronic Effects and StabilitySingle correct
Given below are two statements: Statement I: Hyperconjugation is not a permanent effect. Statement II: In general, greater the number of alkyl groups attached to a positively charged C-atom, greater is the hyperconjugation interaction and stabilization of the cation. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is true but Statement II is false
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is false but Statement II is true
  4. (D)Both Statement I and Statement II are true

Correct answer: (C)

Step-by-step solution →
Q41·Chemistry·Chemical ThermodynamicsSingle correct
Given below are two statements: Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted. Statement II: At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is true but Statement II is false
  2. (B)Both Statement I and Statement II are false
  3. (C)Both Statement I and Statement II are true
  4. (D)Statement I is false but Statement II is true

Correct answer: (C)

Step-by-step solution →
Q42·Chemistry·AminesSingle correct
The sequence from the following that would result in giving predominantly 3, 4, 5-Tribromoaniline is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (C)

Step-by-step solution →
Q43·Chemistry·p-Block ElementsSingle correct
The correct orders among the following are: A. Atomic radius: B<Al<Ga<In<TlB < Al < Ga < In < TlB<Al<Ga<In<Tl B. Electronegativity: Al<Ga<In<Tl<BAl < Ga < In < Tl < BAl<Ga<In<Tl<B C. Density: Tl<In<Ga<Al<BTl < In < Ga < Al < BTl<In<Ga<Al<B D. 1st Ionisation Energy: In<Al<Ga<Tl<BIn < Al < Ga < Tl < BIn<Al<Ga<Tl<B Choose the correct answer from the options given below:
  1. (A)B and D Only
  2. (B)A and C Only
  3. (C)C and D Only
  4. (D)A and B Only

Correct answer: (A)

Step-by-step solution →
Q44·Chemistry·IUPAC NomenclatureSingle correct
What is the correct IUPAC name of the compound given below?
  1. (A)3-Bromo-2-hydroxy-5-nitrobenzoic acid
  2. (B)3-Bromo-4-hydroxy-1-nitrobenzoic acid
  3. (C)2-Hydroxy-3-bromo-5-nitrobenzoic acid
  4. (D)5-Nitro-3-bromo-2-hydroxybenzoic acid

Correct answer: (A)

Step-by-step solution →
Q45·Chemistry·Chemical KineticsSingle correct
Consider the following statements related to temperature dependence of rate constants. Identify the correct statements: A. The Arrhenius equation holds true only for an elementary homogeneous reaction. B. The unit of A is same as that of k in Arrhenius equation. C. At a given temperature, a low activation energy means a fast reaction. D. A and EaE_aEa​ as used in Arrhenius equation depend on temperature. E. When Ea≫RTE_a \gg RTEa​≫RT, A and EaE_aEa​ become interdependent. Choose the correct answer from the options given below:
  1. (A)A, C and D Only
  2. (B)B, D and E Only
  3. (C)B and C Only
  4. (D)A and B Only

Correct answer: (C)

Step-by-step solution →
Q46·Chemistry·Some Basic Concepts in ChemistryInteger
X g of nitrobenzene on nitration gave 4.2 g of m-dinitrobenzene. X = __________ g. (nearest integer) [Given: molar mass (in g mol−1^{-1}−1) C: 12, H: 1, O: 16, N: 14]

Correct answer: 3

Step-by-step solution →
Q47·Chemistry·Chemical ThermodynamicsInteger
A perfect gas (0.1 mol) having Cv‾=1.50 R\overline{C_v}=1.50\,RCv​​=1.50R (independent of temperature) undergoes the transformation shown in the following P-V diagram from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is (−)(-)(−) __________ J (nearest integer). [Given: R = 0.082 L atm K−1^{-1}−1 mol−1^{-1}−1]

Correct answer: 304

Step-by-step solution →
Q48·Chemistry·Chemical ThermodynamicsInteger
A sample of n-octane (1.14 g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is 5 kJ K−1^{-1}−1. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K. The magnitude of the heat of combustion of octane at constant volume is __________ kJ mol−1^{-1}−1 (nearest integer).

Correct answer: 2500

Step-by-step solution →
Q49·Chemistry·d- and f-Block ElementsInteger
Among Sc, Mn, Co and Cu, identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is __________ BM (in nearest integer).

Correct answer: 4

Step-by-step solution →
Q50·Chemistry·IsomerismInteger
The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula C9H12C_9H_{12}C9​H12​ is __________.

Correct answer: 8

Step-by-step solution →

Mathematics — JEE Main 3 April 2025 Shift 2

Q51·Mathematics·Sets, Relations and FunctionsSingle correct
Let f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R be a function defined by f(x)=∣ ∣x+2∣−2∣x∣ ∣f(x)=\big|\,|x+2|-2|x|\,\big|f(x)=​∣x+2∣−2∣x∣​. If mmm is the number of points of local minima and nnn is the number of points of local maxima of fff, then m+nm+nm+n is equal to:
  1. (A)5
  2. (B)3
  3. (C)2
  4. (D)4

Correct answer: (B)

Step-by-step solution →
Q52·Mathematics·Three Dimensional GeometrySingle correct
Each of the angles β\betaβ and γ\gammaγ that a given line makes with the positive yyy- and zzz-axes, respectively, is half of the angle that this line makes with the positive xxx-axis. Then the sum of all possible values of the angle β\betaβ is:
  1. (A)3π4\dfrac{3\pi}{4}43π​
  2. (B)π\piπ
  3. (C)π2\dfrac{\pi}{2}2π​
  4. (D)3π2\dfrac{3\pi}{2}23π​

Correct answer: (A)

Step-by-step solution →
Q53·Mathematics·CirclesSingle correct
If the four distinct points (4,6)(4,6)(4,6), (−1,5)(-1,5)(−1,5), (0,0)(0,0)(0,0) and (k,3k)(k,3k)(k,3k) lie on a circle of radius rrr, then 10k+r210k+r^210k+r2 is equal to:
  1. (A)32
  2. (B)33
  3. (C)34
  4. (D)35

Correct answer: (D)

Step-by-step solution →
Q54·Mathematics·Statistics and ProbabilitySingle correct
Let the Mean and Variance of five observations x1=1x_1=1x1​=1, x2=3x_2=3x2​=3, x3=ax_3=ax3​=a, x4=7x_4=7x4​=7 and x5=bx_5=bx5​=b, a>ba>ba>b, be 5 and 10 respectively. Then the Variance of the observations n+xnn+x_nn+xn​, n=1,2,…,5n=1,2,\ldots,5n=1,2,…,5 is:
  1. (A)17
  2. (B)16.4
  3. (C)17.4
  4. (D)16

Correct answer: (D)

Step-by-step solution →
Q55·Mathematics·Straight LinesSingle correct
Consider the lines x(3λ+1)+y(7λ+2)=17λ+5x(3\lambda+1)+y(7\lambda+2)=17\lambda+5x(3λ+1)+y(7λ+2)=17λ+5, λ\lambdaλ being a parameter, and passing through a point PPP. One of these lines (say LLL) is farthest from the origin. If the distance of LLL from the point (3,6)(3,6)(3,6) is ddd, then the value of d2d^2d2 is:
  1. (A)20
  2. (B)30
  3. (C)10
  4. (D)15

Correct answer: (A)

Step-by-step solution →
Q56·Mathematics·Sets, Relations and FunctionsSingle correct
Let A={−2,−1,0,1,2,3}A=\{-2,-1,0,1,2,3\}A={−2,−1,0,1,2,3}. Let RRR be a relation on AAA defined by xRyxRyxRy if and only if y=max⁡{x,1}y=\max\{x,1\}y=max{x,1}. Let lll be the number of elements in RRR. Let mmm and nnn be the minimum number of elements required to be added in RRR to make it reflexive and symmetric relations, respectively. Then l+m+nl+m+nl+m+n is equal to:
  1. (A)12
  2. (B)11
  3. (C)13
  4. (D)14

Correct answer: (A)

Step-by-step solution →
Q57·Mathematics·Quadratic EquationsSingle correct
Let the equation x(x+2)(12−k)=2x(x+2)(12-k)=2x(x+2)(12−k)=2 have equal roots. Then the distance of the point (k,k2)\left(k,\dfrac{k}{2}\right)(k,2k​) from the line 3x+4y+5=03x+4y+5=03x+4y+5=0 is:
  1. (A)15
  2. (B)535\sqrt353​
  3. (C)15515\sqrt5155​
  4. (D)12

Correct answer: (A)

Step-by-step solution →
Q58·Mathematics·Permutations and CombinationsSingle correct
Line L1L_1L1​ of slope 2 and line L2L_2L2​ of slope 12\dfrac{1}{2}21​ intersect at the origin OOO. In the first quadrant, P1,P2,…,P12P_1,P_2,\ldots,P_{12}P1​,P2​,…,P12​ are 12 points on line L1L_1L1​ and Q1,Q2,…,Q9Q_1,Q_2,\ldots,Q_9Q1​,Q2​,…,Q9​ are 9 points on line L2L_2L2​. Then the total number of triangles, that can be formed having vertices at three of the 22 points O,P1,P2,…,P12,Q1,Q2,…,Q9O,P_1,P_2,\ldots,P_{12},Q_1,Q_2,\ldots,Q_9O,P1​,P2​,…,P12​,Q1​,Q2​,…,Q9​, is:
  1. (A)1080
  2. (B)1134
  3. (C)1026
  4. (D)1188

Correct answer: (B)

Step-by-step solution →
Q59·Mathematics·Definite IntegrationSingle correct
The integral ∫0π/28x dx4cos⁡2x+sin⁡2x\displaystyle\int_0^{\pi/2}\dfrac{8x\,dx}{4\cos^2 x+\sin^2 x}∫0π/2​4cos2x+sin2x8xdx​ is equal to:
  1. (A)2π22\pi^22π2
  2. (B)4π24\pi^24π2
  3. (C)π2\pi^2π2
  4. (D)3π22\dfrac{3\pi^2}{2}23π2​

Correct answer: (A)

Step-by-step solution →
Q60·Mathematics·Sets, Relations and FunctionsSingle correct
Let fff be a function such that f(x)+3f ⁣(24x)=4xf(x)+3f\!\left(\dfrac{24}{x}\right)=4xf(x)+3f(x24​)=4x, x≠0x\ne 0x=0. Then f(3)+f(8)f(3)+f(8)f(3)+f(8) is equal to:
  1. (A)11
  2. (B)10
  3. (C)12
  4. (D)13

Correct answer: (A)

Step-by-step solution →
Q61·Mathematics·Area Under CurvesSingle correct
The area of the region {(x,y):∣x−y∣≤y≤4x}\{(x,y):|x-y|\le y\le 4\sqrt{x}\}{(x,y):∣x−y∣≤y≤4x​} is:
  1. (A)512
  2. (B)10243\dfrac{1024}{3}31024​
  3. (C)5123\dfrac{512}{3}3512​
  4. (D)20483\dfrac{2048}{3}32048​

Correct answer: (B)

Step-by-step solution →
Q62·Mathematics·Sets, Relations and FunctionsSingle correct
If the domain of the function f(x)=log⁡7 ⁣(1−log⁡4(x2−9x+18))f(x)=\log_7\!\big(1-\log_4(x^2-9x+18)\big)f(x)=log7​(1−log4​(x2−9x+18)) is (α,β)∪(γ,δ)(\alpha,\beta)\cup(\gamma,\delta)(α,β)∪(γ,δ), then α+β+γ+δ\alpha+\beta+\gamma+\deltaα+β+γ+δ is equal to:
  1. (A)18
  2. (B)16
  3. (C)15
  4. (D)17

Correct answer: (A)

Step-by-step solution →
Q63·Mathematics·Statistics and ProbabilitySingle correct
If the probability that the random variable XXX takes the value xxx is given by P(X=x)=k(x+1)3−xP(X=x)=k(x+1)3^{-x}P(X=x)=k(x+1)3−x, x=0,1,2,3,…x=0,1,2,3,\ldotsx=0,1,2,3,…, where kkk is a constant, then P(X≥3)P(X\ge 3)P(X≥3) is equal to:
  1. (A)727\dfrac{7}{27}277​
  2. (B)49\dfrac{4}{9}94​
  3. (C)827\dfrac{8}{27}278​
  4. (D)19\dfrac{1}{9}91​

Correct answer: (D)

Step-by-step solution →
Q64·Mathematics·Differential EquationsSingle correct
Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation dydx+3(tan⁡2x) y+3y=sec⁡2x\dfrac{dy}{dx}+3(\tan^2 x)\,y+3y=\sec^2 xdxdy​+3(tan2x)y+3y=sec2x, y(0)=13+e3y(0)=\dfrac{1}{3}+e^3y(0)=31​+e3. Then y ⁣(π4)y\!\left(\dfrac{\pi}{4}\right)y(4π​) is equal to:
  1. (A)23\dfrac{2}{3}32​
  2. (B)43\dfrac{4}{3}34​
  3. (C)43+e3\dfrac{4}{3}+e^334​+e3
  4. (D)23+e3\dfrac{2}{3}+e^332​+e3

Correct answer: (B)

Step-by-step solution →
Q65·Mathematics·Complex NumbersSingle correct
If z1,z2,z3∈Cz_1,z_2,z_3\in\mathbb{C}z1​,z2​,z3​∈C are the vertices of an equilateral triangle, whose centroid is z0z_0z0​, then ∑k=13(zk−z0)2\displaystyle\sum_{k=1}^{3}(z_k-z_0)^2k=1∑3​(zk​−z0​)2 is equal to:
  1. (A)0
  2. (B)1
  3. (C)iii
  4. (D)−i-i−i

Correct answer: (A)

Step-by-step solution →
Q66·Mathematics·Trigonometric FunctionsSingle correct
The number of solutions of the equation (4−3)sin⁡x−23cos⁡2x=−41+3(4-\sqrt3)\sin x-2\sqrt3\cos^2 x=-\dfrac{4}{1+\sqrt3}(4−3​)sinx−23​cos2x=−1+3​4​, x∈[−2π,5π2]x\in\left[-2\pi,\dfrac{5\pi}{2}\right]x∈[−2π,25π​] is:
  1. (A)4
  2. (B)3
  3. (C)6
  4. (D)5

Correct answer: (D)

Step-by-step solution →
Q67·Mathematics·EllipseSingle correct
Let CCC be the circle of minimum area enclosing the ellipse E:x2a2+y2b2=1E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1E:a2x2​+b2y2​=1 with eccentricity 12\dfrac{1}{2}21​ and foci (±2,0)(\pm 2,0)(±2,0). Let PQRPQRPQR be a variable triangle, whose vertex PPP is on the circle CCC and the side QRQRQR of length 2a2a2a is parallel to the major axis of EEE and contains the point of intersection of EEE with the negative yyy-axis. Then the maximum area of the triangle PQRPQRPQR is:
  1. (A)6(3+2)6(3+\sqrt2)6(3+2​)
  2. (B)8(3+2)8(3+\sqrt2)8(3+2​)
  3. (C)6(2+3)6(2+\sqrt3)6(2+3​)
  4. (D)8(2+3)8(2+\sqrt3)8(2+3​)

Correct answer: (D)

Step-by-step solution →
Q68·Mathematics·ParabolaSingle correct
The shortest distance between the curves y2=8xy^2=8xy2=8x and x2+y2+12y+35=0x^2+y^2+12y+35=0x2+y2+12y+35=0 is:
  1. (A)23−12\sqrt3-123​−1
  2. (B)2\sqrt22​
  3. (C)32−13\sqrt2-132​−1
  4. (D)22−12\sqrt2-122​−1

Correct answer: (D)

Step-by-step solution →
Q69·Mathematics·Three Dimensional GeometrySingle correct
The distance of the point (7,10,11)(7,10,11)(7,10,11) from the line x−41=y−40=z−23\dfrac{x-4}{1}=\dfrac{y-4}{0}=\dfrac{z-2}{3}1x−4​=0y−4​=3z−2​ along the line x−92=y−133=z−176\dfrac{x-9}{2}=\dfrac{y-13}{3}=\dfrac{z-17}{6}2x−9​=3y−13​=6z−17​ is:
  1. (A)18
  2. (B)14
  3. (C)12
  4. (D)16

Correct answer: (B)

Step-by-step solution →
Q70·Mathematics·Sequence and SeriesSingle correct
The sum 1+1+32!+1+3+53!+1+3+5+74!+…1+\dfrac{1+3}{2!}+\dfrac{1+3+5}{3!}+\dfrac{1+3+5+7}{4!}+\ldots1+2!1+3​+3!1+3+5​+4!1+3+5+7​+… upto ∞\infty∞ terms, is equal to:
  1. (A)6e6e6e
  2. (B)4e4e4e
  3. (C)3e3e3e
  4. (D)2e2e2e

Correct answer: (D)

Step-by-step solution →
Q71·Mathematics·Matrices and DeterminantsInteger
Let III be the identity matrix of order 3×33\times 33×3 and for the matrix A=[λ234567−12]A=\begin{bmatrix}\lambda & 2 & 3\\4 & 5 & 6\\7 & -1 & 2\end{bmatrix}A=​λ47​25−1​362​​, ∣A∣=−1|A|=-1∣A∣=−1. Let BBB be the inverse of the matrix adj(A adj(A2))\mathrm{adj}\big(A\,\mathrm{adj}(A^2)\big)adj(Aadj(A2)). Then ∣(λB+I)∣|(\lambda B+I)|∣(λB+I)∣ is equal to __________.

Correct answer: -38

Step-by-step solution →
Q72·Mathematics·Binomial Theorem and Its Simple ApplicationsInteger
Let (1+x+x2)10=a0+a1x+a2x2+…+a20x20(1+x+x^2)^{10}=a_0+a_1x+a_2x^2+\ldots+a_{20}x^{20}(1+x+x2)10=a0​+a1​x+a2​x2+…+a20​x20. If (a1+a3+a5+…+a19)−11a2=121k(a_1+a_3+a_5+\ldots+a_{19})-11a_2=121k(a1​+a3​+a5​+…+a19​)−11a2​=121k, then kkk is equal to __________.

Correct answer: 239

Step-by-step solution →
Q73·Mathematics·Limits and ContinuityInteger
If lim⁡x→0(tan⁡xx)1/x2=p\displaystyle\lim_{x\to 0}\left(\dfrac{\tan x}{x}\right)^{1/x^2}=px→0lim​(xtanx​)1/x2=p, then 96log⁡ep96\log_e p96loge​p is equal to __________.

Correct answer: 32

Step-by-step solution →
Q74·Mathematics·Vector AlgebraInteger
Let a⃗=i^+2j^+k^\vec a=\hat i+2\hat j+\hat ka=i^+2j^​+k^, b⃗=3i^−3j^+3k^\vec b=3\hat i-3\hat j+3\hat kb=3i^−3j^​+3k^, c⃗=2i^−j^+2k^\vec c=2\hat i-\hat j+2\hat kc=2i^−j^​+2k^ and d⃗\vec dd be a vector such that b⃗×d⃗=c⃗×d⃗\vec b\times\vec d=\vec c\times\vec db×d=c×d and a⃗⋅d⃗=4\vec a\cdot\vec d=4a⋅d=4. Then ∣a⃗×d⃗∣2\left|\vec a\times\vec d\right|^2​a×d​2 is equal to __________.

Correct answer: 128

Step-by-step solution →
Q75·Mathematics·HyperbolaInteger
If the equation of the hyperbola with foci (4,2)(4,2)(4,2) and (8,2)(8,2)(8,2) is 3x2−y2−αx+βy+γ=03x^2-y^2-\alpha x+\beta y+\gamma=03x2−y2−αx+βy+γ=0, then α+β+γ\alpha+\beta+\gammaα+β+γ is equal to __________.

Correct answer: 141

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Amines 133/186
  • Quadratic Equations 148/186
  • Work, Energy and Power 132/186
  • Some Basic Concepts in Chemistry 129/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Alternating Currents 108/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Electronic Effects and Stability 74/186
  • Hyperbola 77/186
  • Isomerism 51/186
  • Magnetism and Matter 50/186
  • IUPAC Nomenclature 37/186
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